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Rocking stones, balanced in counter-intuitive positions have always intriguedgeologists. In our paper we explain this phenomenon based on high-precisionscans of pebbles which exhibit similar behavior. We construct their convex hulland the heteroclinic graph carrying their equilibrium points. By systematicsimplification of the arising Morse-Smale complex in a one-parameter process weshow that equilibria occur typically in highly localized groups (flocks), thenumber of the latter can be reliably observed and determined by handexperiments. Both local and global (micro and macro) equilibria can be eitherstable or unstable. Most commonly, rocks and pebbles are balanced on stablelocal equilibria belonging to stable flocks. However, it is possible to balancea convex body on a stable local equilibrium belonging to an unstable flock andthis is the intriguing mechanical scenario corresponding to rocking stones.Since outside observers can only reliably perceive flocks, the last describedsituation will appear counter-intuitive. Comparison of computer experiments tohand experiments reveals that the latter are consistent, i.e. the flocks can bereliably counted and the pebble classification system proposed in our previouswork (Domokos et al 2010) is robustly applicable. We also find an interestinglogarithmic relationship between the Zingg parameters and the average number ofglobal equilibrium points, indicating a close relationship between the twosystems.

The mechanics of rocking stones: equilibria on separated scales